Bound State Wave Functions through the Quantum Hamilton - Jacobi Formalism

Abstract

The bound state wave functions for a wide class of exactly solvable potentials are found utilizing the quantum Hamilton-Jacobi formalism. It is shown that, exploiting the singularity structure of the quantum momentum function, until now used only for obtaining the bound state energies, one can straightforwardly find both the eigenvalues and the corresponding eigenfunctions. After demonstrating the working of this approach through a number of solvable examples, we consider Hamiltonians, which exhibit broken and unbroken phases of supersymmetry. The natural emergence of the eigenspectra and the wave functions, in both the unbroken and the algebraically non-trivial broken phase, demonstrates the utility of this formalism.

replaced with the journal version

References in corpus (5)

• Supersymmetry and Quantum Mechanics
• Complex Extension of Quantum Mechanics
• A Study of Quasi-Exactly Solvable Models within the Quantum Hamilton-Jacobi Method
• On Exactness Of The Supersymmetric WKB Approximation Scheme
• Hamilton-Jacobi Formulation of KS Entropy for Classical and Quantum Dynamics

Cited by in corpus (13)

• Quantum Hamilton-Jacobi analysis of PT symmetric Hamiltonians
• Bound States and Band Structure - a Unified Treatment through the Quantum Hamilton - Jacobi Approach
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• The Quantum Effective Mass Hamilton-Jacobi Problem
• Symmetric Tops Subject to Combined Electric Fields: Conditional Quasi-Solvability via the Quantum Hamilton-Jacobi Theory
• Energy spectra of Hartmann and ring-shaped oscillator potentials using the quantum Hamilton-Jacobi formalism
• Shape invariance and the exactness of quantum Hamilton-Jacobi formalism
• Quantum Hamilton-Jacobi cosmology and classical-quantum correlation
• The Generalized PT-Symmetric Sinh-Gordon Potential Solvable within Quantum Hamilton-Jacobi Formalism
• SWKB Quantization Condition for Conditionally Exactly Solvable Systems and the Residual Corrections
• Random Matrices and Quantum Hamilton-Jacobi Method
• Quantum Hamilton-Jacobi Quantization and Shape Invariance